> I would be curious to hear how you are doing your search. [...]
I use a simple brute-force method, that is, I compute the order of
each transform and the number of quarter turns. If there is already
a transform with that order & number of qt, I forget all about it and
go to the next transform.

This sounds to me as though you're assuming that all transforms with a
given order are equivalent as far as deriving further transforms of
other orders go. That is, if you find that a given transform X of
length L has order N, it sounds as though you're assuming that there is
no need to store any other transforms of length L and order N. I'm not
convinced this is justified. If you've found X of (say) length L and
order N, and then find a different Y of length L and order N, I can't
see any justification for the assumption that you can prune the entire
subtree below Y, because if the cycle decompsition of Y is different
from that of X, they may behave entirely differently when followed by
more twists, even though they have the same order.

der Mouse

mouse@collatz.mcrcim.mcgill.edu